Question

Suppose that sin(θ)=6/10 and θ is in the second quadrant. Use trigonometric identities to find the following quantities exactly.

Answer 1

`tan \theta = (sin \theta)/(cos \theta) = (3/5)/(-4/5) = (3)/(5)*(-5)/(4) = -(3)/(4)`


`csc \theta = (1)/(sin \theta) = (5)/(3) \\ sec \theta = (1)/(cos \theta) = -(5)/(4) \\ cot \theta = (1)/(tan \theta) = -(4)/(3)`

Answer 2

sin(theta) = 6/10 and theta is in the second quadrant. Use trigonometric identities to find the following quantities exactly.
---
sin = 3/5
=============
(a) cos(theta)
cos = sqrt(1 - sin^2) = -4/5 (negative in Q2)

-----
(b) sin(2theta) =
sin(2t) = 2sin(t)*cos(t) = -24/25 --> Q3
-----
(c) cos(2theta
cos(2t) = sqrt(1 - sin^2(2t)) = -7/25 (negative in Q3)
-----
(d) tan(2theta) = = sin(2t)/cos(2t) = 24/7 (+ in Q3)